Molecular Attraction, IX. Molecular Attraction and the Law of Cravitation

MOLECULAR ATTRACTION.

IX

MOLECULAR ATTRACTION AND T H E LAW OF GRAVITATION. BY J.

E. MILLS

General Outline of the Paper I . The usual idea of molecular attraction. 2. Statement of the recently discovered law governing molecular attraction. 3. The law expresses the relation between the energy added and the distance apart of the molecules. 4. The law is independent of the mass of liquid taken. 5. Tentative deduction of the law governing the molecular attractive force. 6. Further evidence that the molecular attractive force varies inversely as the square of the distance apart of the attracting particles. 7. The law of gravitation applied to molecular attraction. 8. Application of the law of gravitation to the vaporization of a liquid. 9. The numerator of the law governing the molecular attractive force. IO. The law governing the abstraction of molecular attractive energy from the ether. I I . The law governing the abstraction of gravitational energy from the ether. 1 2 . Possible identity of the laws of molecular and gravitational attraction. 13. The difficulties that arise in explaining gravitation. 14. Newton’s law of gravitation is not a necessary consequence of the motion of the heavenly bodies. 15. Newton’s law of gravitation is not a necessary consequence of the motion of freely falling bodies. 16.Newton’s law of gravitation is not a necessary consequence of the motion of bodies retarded during their fall.

418

J . E. Mills

17. Direct measurement of the attraction of two masses. 18. Comparison of all of the attractive forces. 19. The nature of mass. 20. Proposed modification of the statement of the law of gravitation. 21. Facts in accord with the suggested changes. 2 2 , Sunimary. I. The usual idea of molecular attraction.-Newton thought that the force of gravity was exerted by each individual particle of a mass and made the statement: “Gravitatem in corpora universa fieri.’” It is said that he attempted to apply the law of gravitation to explain chemical affinity and the molecular cohesion to be observed in all liquid and solid bodies, but I have not been able to verify this stakment. Certain it is that the subject was investigated later by Helmholtz and Clerk Maxwell and has been discussed by numerous investigators. The conclusion that the two following facts existed proving that gravitation could not be the cause of molecular cohesion seems to have been almost universally accepted. First: The molecular cohesion was a far greater force than the gravitational force. Second: The sphere of molecular action was small. If the molecular force obeyed the law of gravitation the sphere of molecular action could not remain small but must include the entire mass taken. This is true because the number of the molecules increases as the cube of the distance from a centrally chosen molecule and the gravitational attraction diminishes only as the inverse square of that distance. The fact that the molecular sphere of action is small seemed to demand that the molecular force decrease with the distance a t least as rapidly as the inverse fourth power. The writer desires to point out some recently discovered facts which seem to indicate that the grounds for this conclusion should be very carefully reconsidered. 2 . Statemelzt of the recently discovered law concerning Principia, Book 111, Prop V I I , Coral,

2.

Molecular Attraction

419

molecular attraction.-In an extended investigation of molecular attraction the writer has proved that the following law holds true for normal non-associated liquids : L-EEB I. _ _ _ _ _ = constant, or 1 = ~ ~ ( 3 4 2345). 3\@345 Here I, is the heat of vaporization of I gram of the liquid, E, is the energy spent in overcoming the external pressure as the liquid expands to the volume of the saturated vapor. I, - E, is therefore the so-called internal heat of vaporization and is called 1. d and D are the densities of the liquid and saturated vapor respectively at the temperature of the vaporization. The constant given by the equation is called P f.

I have said that the above law was proved true. I use the word Froved advisedly. Thirty-eight liquids of very different chemical constitution have been investigated' over a very wide range of temperature extending usually from near the freezing point of the liquid to the critical temperature. For thirty of these liquids the very accurate measurements made by Dr. Sydney Young' and his co-workers were available. The proof cannot be quoted here. The eighth paper above cited gives a brief summary of the results obtained. I believe the truth of the law is now established beyond quest ion. Originally the above relation was theoretically derived. The facts prove that the relation is true and its truth is not dependent therefore upon the truth of the theory by which it was derived. Emphasis is laid upon this fact as some seem to ignore the difference and to believe that the conclusions of the writer are based upon theoretical grounds. Jour. Phys. Chem., 6 , 209 (1902); 8, 383, 593 (1904);9, 402 (1905); (1906); 11, 132, 594 (1907); 13, 512 (1909); Jour. Am. Chem. SOC.,31, 1099 (1909); Phil. Mag., Oct., 1910. These papers need revision badly. The eighth paper should be read first, then the last two papers mentioned. The remaining papers can then be briefly examined in the order in which they were written, making allowance for some necessary changes. IO, I

2

Sci. Proc. Royal Dublin SOC.; 12, 3 7 4 (1910).

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J . E. Mills

3. The law expresses the relation between the energy added and the distance apart of the molecules. For a mass of liquid of M grams, containing n molecules each of molecular weight m, if v is the volume of the liquid and V the volume of the saturated vapor, and s, the distance apart of the molecules of the liquid and s, the distance apart of the molecules of the saturated vapor, we have,

Therefore

The above relations assume (see page 423). A. That the molecules are evenly distributed throughout the space occupied by them. B. That the number of molecules does not change. Substituting the above values of d and D in equation I we have 3.

The heat required to change a liquid into its saturated vapor can be directly measured and the energy necessary to overcome the external pressure during the given expansion can be calculated accurately. The internal heat of vaporization must therefore denote the total energy necessary to add to the liquid in order to effect the given change in the distance apart of the particles. Equation 3 expresses therefore the relation between the distance apart of the molecules and the energy which it is necessary to add to them in order to bring about the given change in their distance apart. 4. The law is independent of ;he mass of liquid taken. -It is also an experimentally established fact that the heat of vaporization of M grams of a liquid is just M times as great as the heat of vaporization of I gram of the liquid. Moreover the density of the liquid and the density of the saturated vapor at a certain temperature and pressure are likewise


421

independent of the number of grams of liquid taken. Consequently we can combine the newly discovered law governing molecular attraction with this fact and write, 4. M I = M , ~ ’ ( ~ d a -’4ij). 5.

MI

=

M,uf34G( 5 - 5 ) . $1

$2

5. Tentative deduction of the law governing the molecular attractive force. It is well known that the total energy required for any change is dependent only upon the force overcome, and the distance through which the force is overcome, and is quite independent of the method or mechanism of the change. Denoting the energy by E, the force by f , and the distance by s, we have, 6.

8 = J f.ds.

In the expansion of a liquid the molecular attractive force of any molecule extends doubtless in various directions and to numerous molecules situated at different distances. In determining the total energy required for any given change in volume the action of every molecule upon every other molecule (at least within the molecular sphere of action) must be included in the sumniation. In order to avoid introducing any assumptions no attempt is made at present to unwind this tangle of individual molecular forces. But it is clear that if the action be viewed as a whole and the summation as regards distance be taken between the limits cs, and cs, that the force must follow the law: 7.

so that since ’/, the mass only is moved,

as required. I t will be noticed at once that for any particular liquid p’ is a constant and 3&i is a constant. The meaning

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J . E. Mills

of equation 7 is, therefore, that the numerous individual forces acting between the molecules as they expand from the distance apart s, to the distance apart s, can be replaced by a resultant force acting between the limits cs, and cs, and this resultant force will vary as

cp‘ 3.\inZ M

We will denote

c,u’3&

$2

by p and write 9.

as a law governing the resultant molecular force. Equation g is deduced and stated as a law governing the resultant molecular force. If however M denotes any mass of liquid M might be taken equal to the mass of a molecule m. c would become equal to I and the molecular force proceeding from the individual molecule would therefore be IO.

pnz

f = - = S2

Constant s*

’

the constant varying with different substances. Since the proof of the fundamental equation 4 (or 5) has been obtained only for molecules in bulk this extrapolation of equation g is open to some doubt. The reasonableness of the deduction will however appear later. 6. Further evidence that the molecular attractive force varies inversely as the square of the distance apart of the ataction under ordinary circumtracting partic:es.-Surface stances can be disregarded and the heat of vaporization is therefore independent of the shape of the containing vessels. (This fact is in itself significant. It is not due, as has been supposed, to an inverse fourth power law of the molecular attraction but to the mutual absorption of the attraction by the attracted particles. A t least I believe the facts later cited warrant this statement. Whatever the explanation, the fact i s that the shape of the containing vessels can be d sregarded). It is therefore physically possible and mathematically convenient to have the liquid spherical in shape and to make it expand to a larger sphere in changing to its


423

saturated vapor. To further simplify the treatment we will assume : A. That the molecules are evenly distributed throughout the space occupied by them.-This assumption is probably always more or less untrue. But if the molecules are shifted from their ideal position by reason of the attractive force, the particles would gain in kinetic energy exactly so much as they would lose in potential energy. We may therefore, without error, consider them to be shifted back into their position of even distribution. B. That the number of molecules does not change,Except for associated substances or substances undergoing decomposition, it is generally believed, and the belief rests upon considerable experimental evidence, that the number of molecules in the liquid and in the gaseous condition are the same. The equation is not true where this condition is violated. While I have called the foregoing statements assumptions they are really more in the nature of limitations and do not seriously detract from the strictness of the proof to follow. Thus even if statement A is not true the subsequent proof will hold provided the term " distance apart of the molecules " is understood to mean their average distance apart. Statement B limits the application of the proof to chemically stable non-associated liquids. Under these conditions if s, is the average distance apart of the molecules of the liquid and s, the average distance apart of the molecules of the vapor, it is readily seen from the symmetry of the figure that if any molecule is distant xs, before expansion, after expansion it will be distant xs,. And a little consideration will show clearly that in integrating equation 6 we are summing up a large number of individual actions each of exactly the same character and each represented by

=I xs1

I I.

E

f . ds,

XSP

x being a constant during each integration but varying in

424

J . E . Mills

value for every individual integration. Since x is a constant during each integration and the law of the force remainsthe same during all of the integrations, it is possible to replace all of the n2-n different x’s by their sum, which we will call c and perform but one integration. Therefore the law of the molecular attractive force must be Mp’’ & c i f =_-12.

s2

’

so that

c can hardly be considered a function of the distance apart of the molecules, but is apparently a function of the number within the sphere of molecular action. If c i s not a function of the distance apart of the molecules the force between the molecules must vary inversely as the square of their distance apart in order to produce the observed law. From the point of view of the writer c is dependent on the absorption or neutralization of the ‘‘ lines of force” proceeding from a molecule. The sum total of these is always a constant and the distance at which they are neutralized is proportional to the distance apart of the molecules. c becomes therefore a constant for any particular substance. The idea that the force of molecular attraction cannot vary inversely as the square of the distance apart of the attracting particles is so universal that I stop here t o lay an added emphasis on the above proof. The molecular attraction can vary inversely as the square of the distance apart of the attracting particles. The idea that the inverse square law of the distance is impossible for molecular forces is founded on the error that the forces must vary as the product of the masses of the attracting particles. I would also call attention to the fact that I am not now trying t o explain why the inverse square law of the molecular attraction is true. I have purposely so far said nothing about the mechanism of the action. If some one supposes


425

that the inverse square law is due t o the mutual action of positive and negative forces emanating from a molecule each varying as the inverse fourth power of the distance, the supposition need not, so far as I can see, necessariZy contradict the inverse square law. If the final explanation of the inverse square law proves to be connected with the fact that Descartes’ idea that the total quantity of motion in the universe (including the ether which Leibnitz and modern science failed to include) is a constant, my present statements are not t o be taken as contradictory of such an explanation. I am simply using the nomenclature at present adopted to express a fact. The explanation of the fact I am not just here discussing. Some one may also be troubled by a possibility already noted by the writer in a previous paper, namely, that it is not certain, that the energy per se of a molecule in the liquid condition is equal to the energy of a molecule of its own vapor a t the same temperature and under the same pressure. Therefore it is possible that some of the energy needed for overcoming the molecular attraction during the vaporization of a liquid is drawn from the liquid itself. There is certainly this possibility, and it should be carefully borne in mind that the laws that I am considering in this paper deal with the energy which it i s necessary to add to a liquid during its vaporization and with the corresponding force exerted throughout the molecular distances conditioned by the vaporization. The possibility of an internal source of energy therefore in no degree lessens the finality of the conclusions as made. I might add also that such a concealed source of energy could hardly escape detection unless it followed a law similar to the one under discussion. 7 . The law of gravitation applied to molecular attyaction.The amount of energy that would be required to effect a given expansion if the molecular attraction obeyed the law of gravitation can be readily found. Helmholtz in 1854 investigated the amount of energy that would be given out by the contraction of the sun in order to determine if the energy

J . E. Mills

426

continually radiated from that body could be thus obtained. In this investigation he assumed that the particles of which the sun was composed were at the same temperature before as after the contraction, the excess of energy having been radiated off into space. He also assumed that the force acting between the particles of the sun’s mass obeyed the Newtonian law of gravitation. Hence the investigation was essentially the same as the one at present desired. In order to make possible a better mathematical treatment Helmholtz assumed that the sun was homogeneous in density. Helmholtzlfound that the total heat, W, given out by the contraction of a homogeneous sphere from radius CR, to R, under the influence of a force, f

=

KZ(dM) s2

, between the

elements (dM) of the mass, was equal to 17.

where M, is the total mass of the sphere. In applying the above investigation as given by Helmholtz to the contraction of the saturated vapor into the condition of the liquid it is to be noted that since the volume of a sphere, ‘//,7c Y’, isequal to its mass divided by its density we have, CR,

= ’d$j,

and R,

=

I I

v$.

Also during the

contraction of the saturated vapor to the volume of the liquid the total work done against the attractive forces is equal to M(I, - E,) = M A = W. Therefore substituting these values in equation 17 we obtain 18.

M(I,--I&)

= MI =

W

= 0.9682

KZM61a(3&-sSdij;).

It should be noted that the actual value of this constant as well as the constant of equation 2 5 depends upon the original assumption of Helmholtz that the sphere was uniform in density. I do not see how the transformation from a 11,

* See Moulton’s “Celestial Mechanics,” page 5’8, or Jour. Phys. Chem., I47 (1907).


427

sphere of uniform density to one of uniformly distributed particles could effect any change in the nature of the energy relations involved. So long as a constant mass i s taken equation 18 will reduce t o the form of equation I , namely L-EE, =constant. If, 42--s.\iD however, the mass i s varied, equation 18 informs us that acting under the law of gravitation the work done should vary as the 5/3 power of the mass. It should require 3.2 times as much heat to vaporize 2 grams of liquid as to vaporize I gram. As a matter of fact, we know that it requires only twice as much heat to vaporize 2 grams as to vaporize I gram. 8. Application of the law of gravitation to the vaporization of a liquid.-It is interesting t o take the equation derived by Helmholtz for calculating the energy given out by the contraction of the sun under the action of gravitational force, and by changing the constant, apply the equation to the contraction of a saturated vapor into the condition of a liquid. For the purpose of illuztration isopentane is chosen. In Table I below is given for isopentane the density of liquid and saturated vapor' and also the internal heat of vaporization of I gram.' The equation of Helmholtz has been shown t o reduce t o the form given in equation 18. If 0.9682 K 2 be taken equal to 105.46, and I gram of liquid is used, equation 18 reduces to the yet simpler'form, 19-

W

=

105.46(s&-

3&j) calories.

I give below in Table I under the heading " W " the values obtained from equation 19. Similar comparisons are given for ether and for benzol using for the constants 103.76 and 109.26 res ectively. It is inconceivable to me that the agreement bet een W and L-BE could be accidental. A full investigation of equation 19 for the thirty-eight substances examined is given in J . Am. Chem. SOC.,31, 1099

4

(19.91. Sci. Proc. Roy. Dublin SOC.,12, 374 (1910). Jour. Am. Chem. SOC.,31, 1099 (1909).

J . E. Mills . t .- * *. * r. n .N . . b.o o. m'9 . y0

N

aw

N

a w w

3

t-mo\mo\mw

t-t.ww

t-M

mm*T)N

0 0 0 0 0 0 0 o 00 0 N * w w 0

oooooo N *wcow

e n n u u N N N N N N

B

B

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0


429

The formula used by Helmholtz to represent the energy given out by the contraction of the sun does, by changing the constant and keeping the mass of liquid constant, represent the energy given out by the contraction of isopentane from the gaseous to the liquid condition. And not only isopentane but essentially as well all of the non-associated liquids examined, for similar comparisons for all of these substances have already been published. I have here republished the results for isopentane, ether, and benzene, as coming from Helmholtz’s formula only to emphasize the statement that I do not go beyond the facts when I declare that, as regards variation with the distance, the law of molecular attraction i s identical with the law of gravitation, and precisely the same formula is applicable to both. 9. The numerator of the law governing the molecular force. -The facts to be noted are as follows: MM‘ I . The gravitational law of force is f = K= S2

KMZ __ s2

This law used to calculate the energy given out on the

*

contraction of molecules leads to an equation of the form, energy = cMS’3(’42 -3 dU) . 2. The equation actually governing the energy given out on the contraction of molecules is: energy = MA = ,u’M(~42 - dD). As before noted, this equation, if universally true, indicates that for the molecular force, f

=

7.

3. If a constant mass is taken and the constant suitably altered, the gravitational law, energy = c M6f3(s42- ‘Ji‘D), becomes identical with the molecular law, MA = ,U’M(~&!--- ’QD). 4. The molecular sphere of action is small. The gravita-

tional law of the force would make the molecular sphere of action include the entire mass taken. 5 . Every molecule is subject to the action of attractive forces and itself exerts an attractive force and the attraction between the molecules is therefore of a mutual character. Considering first the meaning of the expression for the

J . E. Mills

430

molecular force,

’F,

it will be seen that p is a constant for

any particular substance, and m is likewise a constant for any particular particle, and therefore for any molecule, f = cons tan t S2

. The molecular force radiating or proceeding from

a molecule is not therefore increased by increasing the number of surrounding molecules. The sum total of the force of a molecule at a given distance is a constant, and if so much of the force is used up in attracting other molecules there remains an exactly equivalent amount less of the force. Molecular force can therefore be viewed as an attribute of the molecule in exactly the same way that chemical force is an attribute of the atom. Just as the chemical force is used up (absorbed or neutralized) by a combination of one atom with another so the force of molecular attraction is absorbed or neutralized by the surrounding molecules. An atom of sodium has a certain amount of “chemical affinity” and an atom of chlorine has a certain amount of “chemical affinity.’’ When these combine the active affinity of each disappears and the sodium cannot continue to attract other chlorine atoms or the chlorine to attract other sodium atoms. The attraction of the combined sodium and chlorine can be regarded as absorbed, neutralized, destroyed, or shielded (the word used makes little difference, seeing that the mechanism of the action is not understood) from other sodium and chlorine atoms. The sphere of action of the chemical force is very small although the force of “chemical affinity” is very great. The absorption of the molecular attraction by the attracted particles in the same way makes the sphere of molecular action small, even though the inverse square law is obeyed by the molecular force so long as its power is operative. Again, the total molecular force varies as a constant times the mass. The constant depends upon the nature of the substance and remains the same constant however much of the substance is taken. The mass is a constant property


431

of every molecule of a particular substance but varies with the number of molecules, that is with the mass, taken. The foregoing discussion of the law of the molecular force proposed has shown that the law very readily explains the facts noted under the headings 3, 4, and, 5, above. It only remains to show that the complex molecular interaction can now be considered and that the fundamental equation can be rigidly deduced from the law of force given provided we assume: C. That the attraction of any molecule i s absorbed at a distance Prof ortional to the distance apart of the molecules.Since the direction of the force is mathematically a matter of no concern we can regard all of the attractive force of one molecule as concentrated upon another molecule a t distance cs,. After expansion this molecule is distant cs, and the energy required for the expansion is

J

- --

20.

ds = p'ms.\rGc Sa

,u'rnc3dm C

I

(.,

-

csz

f)

*

To pull n molecules from each other the total energy is simply n times as great and we have therefore for the total energy, M 13, required to overcome the molecular attraction in vaporizing a mass of liquid M, containing n molecules, each of molecular weight m, 21.

Substituting the values given in equation reduces readily to the form 22.

MA

2

this equation

= M , u ' ( ~ ~ Z -846).

In conclusion therefore, I think that there can be but little doubt that the molecular attraction follows the law, 23. IO. The law governing the swrender of energy from. the ether.-Taking into consideration the fundamental nature

J . E. Mills

432

of the attractive forces it is certainly probable that equation I , A = p ’ ( 3 4 - 3 3 5 ) , will represent under all circumstances, the temperature remaining constant during the expansion, the work done against the force of molecular attraction in moving molecules further apart. Now the further the molecules are moved apart the less becomes the value of D, and D will finally become zero when the molecules have been moved an infinite distance apart. Making, therefore, D equal to zero, we can and remembering that the density, d , is equal to33%/~ write : 24. s4, = constant (For M grams the constant is M,u’~.\‘%) as the very simple form for the law under discussion. This statement means simply this : I n any normal substance the internal heat given out as the molecules approach each other, multiplied by the distance apart of the molecules, i s equal to a constant. The significance of this statement is very great. The potential energy of molecular attraction, since it does not reside in the particles themselves, must reside in the medium surrounding the particles, that is in the ether. (See under heading IS.) Potential energy of attraction is therefore energy due to the position of attracting particles of matter in the ether, and the potential energy of attraction i s a property of the ether. The above law therefore governs the surrender of molecular attractive energy from the ether. I I. The law governing the surrender of gravitational energy from the ether,--The law governing the abstraction of gravitational energy from the ether can likewise be put into a very simple form. Taking equation 17 and making CR, infinite, we have for the energy, E given out on the contraction of a. ’ the mass from an infinite distance, since R, 25. or

E,

s = constant.

=

For M grams the constant is 0.9682 K2M5/a3G 0.9682 K2M2 34;

’


433

where n is the number of molecules in the mass taken. (See also the remark after equation IS.) Comparing equation 24 with equation 25 it will be seen that for any given mass the law governing the surrender of molecular attractive energy from the ether is of precisely the same form as the law governing the surrender of gravitational attractive energy from the ether. The only difference is in the constant involved and this difference depends upon the mass taken. I 2 . Possible identity of the laws of molecular and of gravitational attraction.-The evidence advanced has pointed clearly and almost conclusively to the belief that the three following laws governing molecular attraction and energy changes caused by that attraction are true. (a) f

=

Pm

7, where f

is the molecular force.

( b ) I , s = constant = ,uLL13.JGz M, where I , is the internal energy given out on the coming together of the molecules from an infinite distance t o distance s. ( c ) MA = M,~i’(~42--~4S)-the fundamental law as experimen tally proved. The usual ideas concerning gravitational attraction lead to the following corresponding laws for that force: MM‘ M2 (a’) f = K 2 - y - = K 2 for~homogeneous substances. S

Ems = constant

=

0.9682 K2Mb’334?n =

0.9682 K2M2 3 4 n

*

(c’) E = 0.9682K’M~’3(~42--“”a). The similarity of these laws-they are identical except for the mass and the constant involved-must make one pause and think and think again. Are not the laws really identical? Is not the difference due to some misconception or misconstruction on our own part? Notice that a drop of liquid under the action of molecular forces arranges itself into a sphere. The radius of the sphere may be many thousands of times greater than the radius of the so-called ‘‘ sphere of molecular action.” Notice that the earth also and the

434

J . E . Mills

planets under the action of the gravitational force assume a spherical form, except in so far as modified by their rotational movements. Was not the earth at one time merely a large drop of liquid and was not its shape determined by the same law that determined the shape of the smaller drop? The gravitational attraction applies to every mass and to every measurable particle of every mass, in the universe. Is it possible that the mere subdivision of this mass into molecules should alter the nature of the law? The molecular attraction applies to every molecule in the universe. Is that law altered by the collection of the molecules into an appreciable mass? Would the contraction of a sun made of isopentane differ as regards the nature of the laws concerned from the contraction of a few grams of isopentane in the laboratory? Are there in reality two forces with laws almost, but not quite identical, which apply to the one operation-the aggregation of matter? The idea is not reasonable and there i s but little evidence for it. If the two forces, gravitational and molecular, are identical, which law of force above given is the correct law? I think that the statement of the law of gravitational force as made by Newton needs some modification and that it i s Possible to bring the law of molecular and gravitational force into harmony with the facts and with each other. I only ask that the statement made be judged by the evidence that is, or that can be, presented. It should, a t the outset, be understood clearly that the gravitational law as expressed by Newton and commonly interpreted since his day, cannot, unmodified, be made to apply to molecular attraction for the following reasons : I. The sphere of molecular action would not be small and the liquid could not be regarded as homogeneous throughout. 2 . The heat of vaporization of a liquid would not vary as the mass of the liquid taken. 3. The boiling point of a liquid would vary with the amount of liquid taken and with the shape of the vessel.


435

4. Surface tension phenomena generally would vary with the amount of liquid and the shape of the vessel. 5. The gravitational force as calculated for molecular distances by Newton’s law is not great enough to account for the observed phenomena of cohesion. It should be further remembered that since Newton in 1682 deduced the law of gravitation, all of the attemptsand they have been numerous--to formulate a sufficient cause for the law have completely failed. The attempts have ended not alone in failure to formulate a cause for the law, but in emphasizing, most distinctly, the difficulty of forming such a conception at all. May not the real cause of the trouble lie in the fact that scientists have been trying to explain how a force can be infinitely multiplied and absolutely unaffected by intervening matter, when force with such properties has really no existence? The whole situation merits careful consideration. I 3. The difficulties that arise in explaining gravitation.The difficulties that arise in attempting to explain gravitational force (as that force was understood by Newton and by scientists since his day) have been most excellently summarized by W. B. Taylor,’ and only the unusual length of this paper prevents my quoting his statement of the “Conditions of the Problem” in full. Without reviewing the entire discussion I would place additional emphasis on three facts required by the usually accepted laws of gravitation. First.-The attraction exerted by a particle can be infinitely multiplied merely by the introduction of other particles. If by some act of creation new particles come into existence the former attraction of every particle in the universe is thereby increased. I s it not unreasonable to suppose that a particle could exert its attractive pull upon one thousand, o r one million, or one hundred million, particles and yet always “Kinetic Theories of Gravitation,” Smithsonian report, 1876. The entire paper should be read by those interested in the cause of gravitational force.

436

J . E . Mills

have just as much of its force remaining to exert o n other particles brought within the same distance9 Second.-A particle at the center of the earth attracts a particle at the surface of the earth, or a particle at the center of the sun exactly as if there were n o intervening matter. I s it reasonable that the introduction of particles of matter into the space surrounding a molecule should be absolutely without influence on the wave motion or emanation (or more spiritual essence) which acts as if it Proceeds from the molecule and gives. rise to the phenomena of attraction9 And that this filling in of the space surrounding a molecule with. other particles of matter (or centers of energy, if you choose) should be able to continue, ad infinitum, without disturbing the attractive radiation proceeding from the body? Third.-The attraction is propagated supposedly with an instantaneous velocity, but with a proved velocity’ at least 50,000,000 times that of light; that is, the proof holds unless there is some unknown compensating action. To the reader these difficulties may well appear insurmountable. They have proved equally as insurmountable to every student of the subject. Newton, himself, in his oft-quoted third letter to Bentley, dated Feb. 2 5 , 1692-3, stated: ‘‘ That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a * distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting continuously according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers.” Twenty-five years later, “ a s if driven back from every assault to the only retreat, which in earlier years he had stigmatized as ‘ so great an absurdity ’ that no competent thinker could ‘ ever fall into it,’ he despairingly asks : ‘ Have Taylor: “Kinetic Theories of Gravitation.”

Molecular A ttraction

43 7

not the small particles of bodies certain powers, virtues, or forces, by which they act at a distance. . . . . .What I call “ attraction” niay be performed by impulse, or by some other means unknown to me. I use that word here to signify only in general any force by which bodies tend toward one another, whatsoever be the cause.’ And beyond this point, no human research has yet been able to penetrate. There is no need to review the fruitless effort expended in trying to get an explanation of the gravitational law since the time of Newton. Faraday’ clearly and repeatedly asserted his belief that no force with the properties usually ascribed to gravitation could exist. The question of the truth of the gravitational law cannot be finally settled by an appeal to our minds as to the relative difficulty or ease of the conception, though such an appeal is not without value. Let us proceed further to examine in detail the evidence for the law. 14. Newton’s law of gravitation is not a necessary consequence of the motion of the heavenly bodies.-Kepler deduced from the observations of Tycho Brahe and his own three empirical laws governing the motion of the planets about the sun. Newton perceived that these motions of the planets about the sun and the motion of the moon might be determined by the action of a force differing in no substantial respect from the force of gravity as exhibited on the earth. He investigated this brilliant conception and finally stated the universal law of gravitation as causing the observed planetary motions, g

=

MM‘

k 7 .

Newton did not know the mass of the earth, or of the moon, or of the sun, or planets. He could not therefore prove the numerator factor of his law correct so far as the masses of the heavenly bodies are concerned, and we are to-day as totally without proof. All of Kepler’s laws follow on the assumption of a central acceleration varying inversely as the square of the a

Taylor: “Kinetic Theories of Gravitation,” page 5 . “Essay on the Conservation of Forces,” and other writings.

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distance from the center. The fact that this central acceleration varies as the product of the masses of the attracting bodies was a pure assumption, so far as the heavenly bodies are concerned, made because Newton saw clearly that all masses appeared to be concerned in such mutual attractions. The mass of the earth was really determined for the first time by Maskelyne in 1774 who weighed the earth against a mountain (by measuring the deflection of a plumb-line) and obtained its weight on the assumption that the law of gravitation as stated by Newton was true. Since that time various investigators have made use of four methods for determining the mass of the earth but in all of these methods the truth of Newton’s law of gravitation i s assumed. Really only the attraction or acceleration between various masses is directly determined and the mass is calculated on the assumption that Newton’s law of gravitation is correct. When we consider the various methods of obtaining the masses of the other heavenly bodies we find always a similar condition. The relative amount of the attractions are determined and the masses are calculated on the basis of Newton’s law. Astronomical data gives absolutely n o evidence to show that gravitational attraction varies as the product of the masses of the attracting bodies. It does prove that a force of a definite and apparently unchanging magnitude emanates as if from the center of each heavenly body within the limit of investigation and that this force varies inversely as the square of the distance from its origin. The magnitude of the force exerted depends upon some property of the body. Astronomical data does apparently further prove that this force of gravity cannot be shielded, or refracted, and that its action is instantaneous throughout all ascertained distances. Thus the passage of the moon between the sun and the earth does not alter in the slightest degree the relative motion of the sun and the earth and therefore apparently does not disturb the attraction which exists between them. This remarkable circumstance (equally true for all similar cases) has doubtless kept many from questioning the truth


439

o f Newton’s statement o f the gravitational law. An explanation of the actually observed facts is suggested later. 15. Newton’s law of gravitation i s not a necessary consequence of the motion of freely falling bodies.-If bodies, initially at rest near the earth’s surface, fall freely towards the earth under the influence of the gravitational attraction the following laws apply: Let v = velocity acquired, a = acceleration produced by gravity, t = time, s = distance traversed. Then, 26.

at2.

v=at; d = - , a s = - . 2

V2

2

These laws and these laws alone are sufficient to determine the motion of bodies near the earth free to fall under the action of gravitational attraction. Motion on an inclined plane and the motion of pendulums can be regarded as falling under this head. It should be noticed particularly that the mass o f the body nowhere enters into thee quations. That is to say a feather, a gram o f aluminum, and a pound o f lead, in a vacuum, all fall a t exactly the same rate, and that rate is in no sense dependent upon their relative mass. It should be borne in mind that if during its fall the mass of the lead were altered to that of the aluminum, or to that of the feather, the change of mass could not be detected by any observation upon the motion of the lead.’ It is therefore perfectly clear that no observation of the motion of a body falling freely towards the earth will give any evidence as to the mass of the body. This statement as has already been shown applies also to the motion o f the heavenly bodies. Objection has been raised to this statement on the ground that the alteration of mass is a purely hypothetical question and also on the ground t h a t the conservation of energy must be considered. I do not believe that the alteration of the mass is a purely hypothetical question. I suspect very strongly t h a t it does actually take place and I am here giving one reason why we have heretofore failed t o detect it. As regards the conservation of energy, if the kinetic energy of a body is due to its motion, my very point is that this motion is not changed. If as I think more likely the kinetic energy of a moving body is more or less a property of the ether surrounding the body then the energy is adjusted when the ether condition is adjusted-that is probably completely only when the system becomes static.

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Newton’s calculation showing that the moon “fell” towards the earth required no knowledge of the mass of the moon or of the earth. It did prove that the earth’s attraction extended to the moon and that this attraction varied inversely as the square of the distance from the center of the earth. A cannon ball a t the distance of the moon once given the velocity of the moon would follow its orbit very nearly. The difference observed would be due to the fact that the moon and the earth revolve around their common center of gravity which would be changed by the substitution of the cannon ball for the moon. Now o n the supposition of Newton’s law of gravitation the relative mass of the moon and earth can be obtained from this fact. Similarly the relative mass of the planets is obtained from the divergence froni Kepler’s third law. It is thus a little curious that our knowledge of th2 relative masses of the heavenly bodies is largely due to their divergence from the very laws Newton’s law was advanced to explain. The divergence of course likewise takes place in accordance with Newton’s law. 16. Newton’s law of gravitation i s not a necessary consequence of the motion of bodies retarded during their fall.-Imagine two equal masses of say 99 grams each connected by a cord and balanced by passing the cord over a nearly frictionless pulley free t o revolve. Now motion in such a system can be started by placing a sniall rider, let us say of 2 grams, upon one of the masses. The mass will descend undzr the action of the gravitative force exerted by the earth upon the mass of 2 grams. The velocity acquired will however be only I/IOO of the velocity acquired by the a-gram mass if it be. allowed to fall freely. And in general, it can be thus shown that the force of gravity i s proportional to the mass of the attracted body. The same fact may also be demonstrated by measuring the gravitational attraction upon any body and then determining the inertia of the body when it is subjected to motion in a horizontal plane. Always the force of gravity appears to be proportional to the inertia of the body. But this fact, so far from constituting a proof of Newton’s law of


441

gravitation, is a proof only of the law of molecular force given, namely, force

=

constant X mass

----.

SZ

17. Direct measurement of the attraction of two masses.When Newton proposed his magnificent generalization he had n o proof whatever that the gravitational attraction did vary as the product of the masses of the attracting bodies. The attraction of two bodies, the masses of which could be independently determined, was not measured by any experimenter for nearly a hundred years after the law had been proposed. Newton saw that the attraction of gravity apparently extended to all bodies, that it apparently could not be shielded, deflected, or absorbed in any way, and that the earth’s attraction, at least for bodies near the earth, varied as the mass of the bodies. From these facts Newton made his generalization. In attempting to find the constant of gravitational attraction the attraction of two masses has been directly measured by a number of experimenters using several different methods. The experiments are difficult in the highest degree and naturally the results did not at first agree well with each other. But the difficulties have been gradually overcome and reliable measurements have now been made of the attraction of two masses at known distances under circumstances permitting of the elimination of the numerous disturbing elements. The fact that these experiments were performed under diverse conditions, with masses of varying size and substances, at varying distances, and yet give agreeing (considering the difficulty of making accurately the measurements involved) values for the gravitational constant k, constitutes the sole proof existing to-day, so far as the writer is aware, of the truth of Newton’s statement that substances universally attract as the product of their masses. The proof that has thus accumulated cannot be lightly put aside. An interesting account of these experiments is to be found in “The Laws of Gravitation,” dy A. S. Mackenzie. The agreement shown by these experiments is one fact

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that must be explained in explaining gravitation. I will refer to these experiments later. 18. Comparison of all of the attractive forces.-The nature of the gravitational and of the molecular attraction is a very fundamental question. The nature of matter, of inertia or mass, the nature of the other attractive forces, and the nature of the ether must all be considered to some extent a t the same time. The table below gives the usually accepted belief as to the action of the attractive forces. The general resemblance between these forces is so striking, I think, as to warrant a very serious consideration of any idea which leads to the belief that all of the forces do not follow the same law. Are they not perhaps all, in fact, one and the same force? Are not the apparent exceptions to a complete similarity between the action of the forces due to our lack of knowledge, or to a wrong understanding and interpretation of the facts involved? In seeking an answer to these questions the interpretations suggested below of certain facts are new, and in order to prevent confusion a general discussion of the table precedes the more detailed consideration of the facts. All of the attractive forces appear to proceed from some particle or mass of matter as a center and to be exerted upon some other particle or mass of matter across an intervening space which is supposed to contain ether. Thus always in the action of the attractive force at least two particles are concerned and these two particles possess, because of their mutually attractive force, a so-called potential energy, which can be obtained from the system by causing the particles to approach. Without making any further supposition whatever, fundamental mechanical principles being true, as to the nature of the particles, of the ether, or of the attractive force, it is clear that this potential energy does not reside in the two particles from which the force appears to proceed, for these particles can be supposed at rest and therefore devoid of all energy per1 se. (If when the particles are at rest, they possess internal motion, it can hardly be supposed that the internal motion is changed by their approach. Yet


u

1

u

2 2

.Y

443

Law of variation with the distance

B 0 *

1 11

/

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J , E. Mills

perhaps this possibility should not be regarded as eliminated.) This potential energy, since it does not reside in the particles themselves, must reside in the medium surrounding the particles, that is in the ether. Potential energy of attraction is therefore energy due to the position of attracting particles of matter in the ether, and the potential energy of attraction is a property of the ether. This view is pretty generally accepted. It is equally clear that this energy of the ether exists or exists in an available form, solely on account of the presence of the attracting particles. The attraction must therefore be caused by some interaction between the attracting $articles and the ether. While two particles and the ether are necessary t o the phenomena of attraction, it is quite clear,l that the two particles are not necessary for the interaction between the matter and the ether. That is, each particle alone must interact with the ether in such manner as to produce a modified condition of the ether in its neighborhood. Two or more “ modified conditions” of the ether produce an attraction between the particles causing the “ modified conditions,” and the attraction is due to some connection between these modified ether conditions. I t is clear that if one particle alone in the ether be considered, the total effect of its interaction with the ether i s a proper measure of its potential attractive energy, which under these conditions becomes a constant and definite property of the $article. Without knowing, or at present considering, the niechanism of the interaction between the ordinary particle and the ether yet a further conclusion can be drawn. Consider two particles at an infinite distance apart, each particle being surrounded with its modified sphere of et,her. Probably these “ modified spheres of ether proceed from a particle somewhat as does light from a central source of light. Under ’)

1 The author holds the belief that two particles of ordinary matter or of ether cannot exert any action upon each other across an absolutely empty (devoid of matter and of ether) intervening space. To attempt to justify this belief would lead to an examination of the foundations of thought, mathematics, and science. Such an examination would lead us too far from the immediate object of the present paper and cannot be undertaken here.


445

the influence of their mutual attraction caused by these modified spheres of ether the two particles commence to approach each other and gain in kinetic energy. The ether loses therefore a corresponding amount of energy and must suffer change to a corresponding extent. The loss of this energy by the ether must be to that extent a reversal of the “modified condition of the ether” caused by the particles of matter; for the cause of the attraction, as has been seen, lay in this modified condition of the ether and when the cause produces a change the cause must itself suffer an equal opposite change. If this does not happen there would be a creation of energy, I n fact the modified spheres of ether can be regarded as produced by the interaction between the particles and the ether and as representing so much available energy, aird if some of this energy i s used up, the amount of energy remaining must be diminished by a n exactly equivalent amount. The attractive force, which is a manifestation of this energy, must be subject t o a corresponding limit. That is, the attractive forces, whatever their nature, whether chemical, molecular, magnetic, electrical, or gravitational, which proceed from a particle are definite in amount. If this attraction i s exerted upon another particle the amount of the attraction remaining to be exerted upon other particles i s diminished by a n exactly equivalent amount. Strenuous objection has been raised to this sentence and I have been accused of confusing force and energy. I am not confusing the two. I think force in its last analysis has to do with the quantity of motion transferred per unit of time. I do not consider this idea of force heretical. When the totality of a force is considered per unit of time (as is here done) it will be seen that the quantity of motion transferred can be increased only by increasing the velocity of the moving particles or by altering their distance apart (or their number per unit of volume, which is the same thing). Both of these operations (alteration of velocity or distance apart) would require the expenditure of additional energy. Where the eiicrgy is fixed and a definite system is considered the total

446

J . E . Mills

force is also constant. I have been cited to the hydraulic press, etc., as illustrations of how force can be multiplied. The total force in a hydraulic press has to do with the total motion exchanged among the molecules of the liquid used. For a given press the total force of the system i s constant unless the amount of liquid used, the temperature of the liquid, or the distance apart of the molecules are altered, and aZZ of these alterations require the expenditure of energy. When we keep the conditions in the press the same the force exerted at one end is multiplied at the other because we consider only a part of the total force and that part as acting on different areas. There can really be no multiplication of the total force except as above stated. I see no reason whatever for attributing “powers” t o a molecule which are not possessed by any mechanism whose real nature we are able to understand. The disturbance set up by the interaction of a molecule and the ether is in my opinion perfectly definite in amount for a given condition of the molecule and the ether, and this disturbance represents a certain amount of energy and a certain total and perfectly definite transference of energy per unit of time, which definite amount of force can be used (that is, exerted on ordinary matter), but once used does not continue available. In my opinion the idea that a definite electrical charge on a definite particle represents a definite amount of energy necessitates the above conclusion regarding the constancy of the electrical force proceeding from the charged body, similarly as regards magnetic forces. Hence it will be noticed that the gravitational force offers the only pronounced exception to a general resemblance of the forces. Perhaps it is best in this connection t o call attention t o the following points : I . As regards the positive and negative tendencies of the forces, chemical, magnetic, and electrical forces show decided evidence of directive action. It is usual, moreover, to distinguish between positive and negative electricity, positive and negative poles of a magnet, and positive and negative elements, as indicating some difference in the kind of attractive force which they exert. As evidence of variation in the intensity of the-moleciilar forces-wich tjleir spatial


447

arrangement around the molecule, might be cited the phenomena of crystalline form, of water of crystallization and molecular combinations in general, and also those cases where a liquid appears to show a definite and symmetrical structure. The evidence that the molecular forces show positive and negative tendencies is not convincing and so a question mark is inserted in the table t o indicate our lack of knowledge. With gravitational force there is no evidence showing positive and negative tendencies of the force. 2. Some might be inclined t o doubt the statement that temperature has no effect upon chemical affinity. This fact is however almost beyond doubt.’ Almost equally beyond doubt change of temperature has per se no effect on magnetic and electrical forces, but being unable t o cite direct experiments upon this point the writer has used question marks in the table. 3. The velocity of propagation of a chemical reaction is of course an altogether different quantity from the velocity of propagation of the chemical force itself. There is no evidence as t o the rate of propagation of either chemical, molecular, or magnetic forces. The velocity of propagation of gravitational force is discussed in the reference already given.2 Electromagnetic waves travel with a velocity of 186,000miles per second. I have taken this as indicating the speed of propagation of electrical force through the ether. 4. The law of variation of the chemical force with the distance apart of the atoms is unknown, but that this force does vary as some function of the distance apart of the atoms concerned has, I think, been already shown by the work of Richards3 and T r a ~ b e .The ~ latter says: “Wie zron mir zuerst festgestellt wurde, ist der Raum e i w s .4toms keine IConstaizte, s o n d e m aiidert si& V O I I Stof 276 Stoff wnd ist urn so kleiver, j e grosser die .ifinitat des betrtffciiden. Atomes zu den 4tonicn ist, init welchen es i v unmittclbarer ~ V/~rbind~tng steht. Die Kontraktion der Atoine ist dah.er ein unniittebbares Mass der Afinitat.” Concerning Traube’s claim t o priority in this discovery see remark by R i ~ h a r d s . ~While I prefer not t o accept the conclusion of these investigators t h a t the atoms themselves suffer a contraction, I cannot doubt from the evidence that they have brought forward that the chemical attraction between atoms is one of the deciding factors as to the distance apart of these atoms when combined into a molecule. That is to say, the distance apart of the atoms is some function of the chemical afinity. The problem is as yet too complicated to permit of finding the law of the attraction, and at present I must limit myself to the statement t h a t the inverse square law of the distance is possible also with this force. The rather widespread idea that the inverse square law is not possible for chemical force rests upon the same error already discussed for molecular force. The investigator9 have not taken into consideration the mutual absorption or cancellation of the force by the atoms when they unite.

e

Trans. Am. Electrochem. SOC.,14,35 (1908). Taylor: “Kinetic Theories of Gravitation.” Proc. Am. Acad., 37, I (1901); 15 (1902);38, 7 (1902);39, 23 (1904). Zeit. anorg. Chem., 40, 380 (1904). Proc. Am. Acad., 39, 23, 583 (1904). See for instance Helmholtz: Jour. Chem. SOC.,39, 2 7 7 (1881).

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448

In considering the numerator factor of the forces three circumstances are worthy of attention : First. Except for the gravitational force, the numerator factor of the force is supposedly bound up with the nature of the force itself.-Thus when we speak of the “electrical” force the numerator factor has to do with the “electrical” charge; when we speak of the “ magnetic ” force the numerator factor is the “magnetic” strength of the pole; when we speak of “ chemical ” or “ moIecular ” attraction, the numerator factor is supposedly dependent upon the “chemical” affinity or the nature of the molecule ;” when however we speak of gravitational force, it is usual to regard the numerator factor of the force as “ mass,” and as a property therefore distinct from and independent of gravitation. Is not “ mass ” really a gravitational ” charge? Second.-Just as the condition of an electrical charge can be considered as dependent upon two factors, a capacity factor C, and an intensity factor, the voltage V, so possibly the “ gravitational charge ” or mass, would be dependent upon two similar factors. Siniilarly for the numerator factors of all of the forces. Third.--If one attempts t o consider what changes must be made in the numerator factor of the forces in order t o derive a common expression for all of the forces, one starts with the broad idea that a force is measured by the effect which it produces. There is no law as to the conservation of force, but there is a law as to the conservation of energy. Granting the conclusion already drawn that the modified sphere of ether surrounding a particle represents a definite amount of energy belonging to the particle and that this potential energy of the particle is transformed into kinetic energy of motion by some interference of two such spheres, then it is clear that this interference of these modified spheres of ether constitutes the force of attraction acting between the particles. Now since force is transference of energy the total attractive force of a particle is definite in amount. If therefore a portion of this attraction is expended upon one particle there remains exactly I‘

‘ I


449

an equivalent amount less to be expended upon the remaining particles. Consequently the attractive force exerted can be measured by the amount of the neutralized force. From this point of view the usual ideas of the attractive forces could be expressed : Force

=

amount of attraction neutralized a t unit distance

amount of attraction neutralized a t unit distance S2

It seems perfectly reasonable that the attractive force should vary with the amount of the attraction absorbed at unit distance but why should the force vary as the product of the amounts so absorbed? Moreover the above expression makes the mass of a particle proportional to the amount of the attraction absorbed. Is this idea of mass further supported by the facts? The close relationship of magnetic and electrical forces is well known. The probability of a very close relationship or, identity, of chemical and electrical forces is now hardly doubted by any one. Many chemists at heart consider molecular and chemical forces as of probably identical origin and character. Recent work shows that the motion of electrical charges may account for mass. Is it then too much to suspect that gravitation belongs also within the fold? And is it too much to ask that more serious attention be given t o the possible ultimate identity of all of these forces? 19. The nature of mass.-Each of the three following definitions of mass are sometimes given : A. Mass is quantity of matter. B. The unit of mass is that quantity of matter which will counterpoise in a balance a certain standard mass known as a standard pound or gram. C. Mass is inertia-resistance to motion. This is the modem definition and finds expression in the formula, energy = M. a. s. = 1/2 MV2, or mass X acceleration X distance traversed = mass X (velocity acquired)2. As regards definition A, compare a mass of I gram of lead with a mass of I gram of aluminum. There is not, so

\

450

J . E. Mills

far as the author knows, one iota of evidence, save in the suggestiveness of the periodic table of the chemical elements, as to whether the gram mass of aluminum and of lead contain equal or unequal amounts of the “ultimate material” of which both may be composed. And there is no way of finding out unless the aluminum and the lead can be decomposed into the ultimate constituents of which they are made. The first definition should, therefore, for the present, be banished from science. Definition B is founded on the fact that mass is proportional t o weight, or equal to

weight and is therefore a acceleration’

deduction from Newton’s law of gravitation. Adopting the third definition that mass is inertia, or resistance to motion, it is certainly reasonable to consider the resistance to motion in the ether to be in principle the same as the resistance to motion in other media. If one tries t o move a particle from a bar of iron, or from a piece of lead, the resistance to the motion is great. Why? Because the attraction of the particle for the surrounding particles is very great. If this attraction is overcome it becomes very easy to move the particle. If one tries to pull a boat t o land, the inertia of the boat does not depend entirely upon its mass but upon the resistance the water offers to its motion. The motion of matter through the ether must be similar. T h e inertia of a body i s the amount of resistance offered by the ether to the motion of the body. The usual idea of the motion of matter through the ether has more or less neglected three facts, each of great importance. I. The ability of a particle to accelerate other particles towards its own position (i. e., to attract) must depend o n the irzertia of the particle as one factor.-Mach declares’ that the concept of mass as inertia renders unnecessary the special enunciation of the principle of action and reaction. Why did not Mach go one step further and apply his statement to the gravitational force? Science of Mechanics, page

220-5.

Moleculay Attraction.

451

Consider a particle with the ability to attract but possessed of no inertia, and attempt to apply the principle that action and reaction must be equal and opposite. The particle without inertia and its attractive mechanism would be a t once moved to the position of the attracted particle at the first effort to preserve the principle of action and reaction. A little consideration will show clearly that the attraction, the inertia, and the principle of action and reaction, are but phases of the same phenomenon. Their relationship will appear more clear from a concrete example. Suppose a man in a boat by means of a rope attempts to pull a man on land into the water, The man in the boat, no matter what his strength, cannot produce an effect greater than that allowed by the inertia of his boat. His greater effort would only result in drawing his own boat the faster towards land, while the man on land retains, perhaps, almost his same position, due to the fact that he can suitably brace himself so as to produce in himself a relatively great inertia. If the man on land is immovably braced to the earth the principle of action and reaction is not violated. The entire earth will be slightly moved so that the center of gravity of the entire system-earth, water, and boat-is preserved. If both men are in boats both boats would move. The inertia of one boat, times the distance through which it moves, is equal to the inertia of the other boat times the distance through which it moves, or obviously, Is = 1’s’. Now consider carefully the boats and the rope. If the rope is slack there is no pull (attraction) between the boats and there is no inertia actively displayed. If now the man in boat I’ pulls the rope supposed attached to boat I, he “ a t tracts ” boat I and causes at the same time a display of interia in his own boat. If the rope is attached to boat I’ and the puIling is done by the man in boat I then boat I “attracts” boat I’ and inertia is brought into play in boat I. In each case the pull upon the rope (the attraction) is possible solely because of the inertia of the boat from which the pull proceeds. The attraction and the inertia are different ends of the

452

,

J . E. Mills

The man in either boat might say “ I can pull (attract) the other boat because of the inertia of my own boat.” A man on land would say : “ The rope is stressed, both boats are attracted, and both boats possess an inertia which depends on the boats themselves and on the surrounding water.” The case is exactly similar when two particles attract each other except for the fact that while the rope is the ether, the ether likewise represents the water, and is therefore one factor determining the inertia (the other factor being the nature of the particles, probably their size, if they are “ultimate” particles). Therefore, while in the case of the boats there is no necessary relation between the strength of the man in the boat and the inertia of his boat, in the case of the attracting particles, the attraction of a particle and its inertia are proportional, both being determined by the ether surrounding the particle. Quite possibly the total attractive force of a particle depends upon the total ether surrounding the particle. Its inertia towards any given attraction depends upon the ether encountered in its motion and is therefore a function of its “front.” Its acceleration is produced by the pressure of the ether from “behind.” Different masses at the same distance from the attracting body have the same acceleration because the ratio of the ether pressure “behind” to the ether resistance in “front” is the same. 2 . Light, heat, magnetic and electrical phenomena, also molecular and gravitational as well, show that under certain circumstances ether can react strongly with ordinary matter. Yet the ether is said to offer no resistance to the motion of a heavenly body or to the motion per se of other bodies. This is a remarkable, and a remarkably neglected, state of affairs. 3 . The mass or inertia of a body is said to depend upon its resistance to motion in a horizontal plane and the idea and measure of mass is said to be altogether independent of the law of gravitation. This is not true as will appear upon closer inspection. The horizontal plane is defined with same rope.

Molecular A ttractiolz

453

reference to the center of gravity; that is, the horizontal plane is made to follow the curvature of the earth. Then motion in this plane is supposed to be free from the influence of the earth’s attraction. This is unfortunately untrue, since the body will continue in motion upon the plane thus defined (even were there no air and normally no friction) only with one particular velocity. If the body is given too small a velocity it will at once press upon the plane and if it be given too great a velocity it will at once leave the plane. When the body is given such velocity that it will retain its position upon the so-called ‘‘ horizontal ” plane it is virtually falling around the earth.‘ Our measure of mass, therefore, so far from being free from the influence of the surrounding field of force is essentially determined by that field of force. The idea that mass, even when it occurs in the expresMv’ as one of the terms defining energy, cannot be sion defined or measured so as t o get rid of gravitational attraction as a determinative factor will probably meet with opposition. It is well, therefore, here t o recall the historical dispute over this expression between Descartes and Leibnitz and their followers-a dispute which lasted for seventy years and continues even yet to break out periodically. Descartes thought that the quantity of work in a body should be measured by the quantity of motion ( M V ) , Leibnitz that it should be measured by the vis viva (MV2). Mach in his wonderful book “The Science of Mechanics” gives a history of the dispute well worth reading and says: “Similarly, the capacity of a moving body for work, whether we measure it with respect t o the time of its action by its momentum or with respect t o the distance through which it acts by its vis viva, has no significance referred t o a single body. It is invested with such, only when a second body is introduced, and in the first case, then, it is the difference of the velocities, and in the second the square of the difference that is decisive. Velocity is a physical level, like temperature, potential funcis new.

This fact hardly needs proof here. The application of the fact alone For proof see almost any book on analytical or celestial mechanics.

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tion, and the like.”’ (English translation, page 325.) This statement and the grounds for the statement should be carefully digested. Some one will ask: “ If the ether offers a resistance to the motion of matter why does not the earth, etc., burn up on account of the energy that would be developed through friction?” The answer is that if two bodies approach each other under the action of gravitational attraction, energy is developed and is stored up in the bodies or in the surrounding ether. It is thus that kinetic energy is made. In my opinion a body without any attractive force would not have mass in the usual sense of that term. If in motion its energy would be measured by m’v and not by 1/2 MV2 where m‘ is a capacity factor differing from mass as usually defined. Moreover, since gravitation acts continuously, ordinary mechanical principles holding true, we know that the action must be dynamic in its nature. There is a continual exchange of energy between the matter and the ether. Uniform motion in a circle simply means that the body is giving out exactly so much energy as it absorbs. However, I am not discussing the possible mechanism of the gravitational action in this article, except where it is essential to do so to avoid a misunderstanding of my point of view. In conclusion, therefore, I think that mass is proportional to the resistance offered by the ether to the motion of a body and that the amount of this resistance is proportional to the amount of the attraction absorbed under a specified condition. The attraction and the mass are a sort of action and reaction due to the same cause, or rather they both depend upon the amount and the condition of the ether with which the body Comes into contact. Mass is a gravitational charge. A body alone in space could not possess mass any more than a body alone in space could possess an electrical charge. Per-

’ Mach agrees with Leibnitz and accepted scientific usage and thinks Descartes has been proved wrong. But i t is worthy of note that if the ether has momentum Descartes may yet be right and his idea may be the more universal and fundamental of the two. I think this point may prove of importance in discussing the mechanism of gravitational action.


455 MM’

haps mass M’ in the gravitational formula, ~2, could be thought of as a positive charge (it has to do with the attraction), mass in the kinetic formula, 1/2 Mv2, as a negative charge (it has to do with the inertia). They are obverse and reverse of the same thing. Perhaps this particular idea of mass is not essential to the reconciliation of the laws of gravitational and molecular attraction, but I have felt that the succeeding statements could not be properly understood without some explanation of my point of view regarding mass. 20. Proposed modification of the statement of the law of gravitation.-In order to make the statement of the law of gravitation accord with the law of molecular attraction, if the views expressed in this paper are correct, two changes in our usual conception of the gravitational law are necessary : First. The total attractive energy of a given body i s to be corzsidered a constant.-It is a property which belongs essentially to the body and to its surrounding ether. This energy is changed into kinetic energy upon the approach of other bodies and may then be given out as heat, etc. Second. Mass in the usual sense i s a relative and not a n is proportional to the atabsolute property of a body.-It tractive forces to which the body is subjected. The first change has to do with the totality of the attractive force. The second has to do with the distribution of this perfectly definite force. As regards the totality of the force, if the particle or mass be supposed so surrounded with other matter that its total field of force is neutralized a t distance s, then we may write as the law governing the force exerted by the particle, 27.

Force

=

Pnl

7,

where JI, is, as before, an intensity factor, and where m is a factor identical with, or proportional to, ordinary mass.

456

J . E. Mills

This statement is intended t o hold both for molecular and for gravitational force. We could conceive that the total force proceeding from a particle was absorbed by one neighboring particle (as was done in section 9) a t the distance s, and so long as we are considering the total acting force or total obtainable energy, no error is committed But as a matter of fact we know full well that the total attractive force of one particle is not confined to a single neighboring particle. How then is this perfectly definite force distributed? Certainly t o all of the particles in the immediate neighborhood, quite possibly to every particle of matter in the universe; for the statement made that equation 2 7 applies to the gravitational force is not t o be regarded as necessarily a contradiction of the idea that every particle of matter in the universe attracts every other particle. It is only to be regarded as necessarily a contradiction of the idea that every particle of matter in the universe attracts every other particle as if no other particles existed. The difference can be made clear by analogy. The attractive force is a property of the ether and one molecule or body by affecting the condition of this ether may affect every other molecule or body. Just as a fat bather a t Atlantic City may cause the water to rise in the ocean and produce an infinitesimal influence extending throughout the entire ocean even to a bather at Brighton Beach. But if some sea spirit by a process of integration, or otherwise, collects this widespread influence, he will find it definite in amount, and t o consist of two factors-a capacity factor determined by the size of the aforesaid fat bather, and an intensity factor determined by his average depth of immersion. There is just so much ocean displacement and if one sea spirit makes use of a portion of that displacement he diminishes the total by an exactly equivalent amount. The mistake that has been made in the interpretation of the gravitational phenomena is not necessarily' in the statement that' every particle attracts 1 Perhaps the attractive influence is exerted fairly directly, perhaps by proxy. It is interesting in thinking of the possible mechanism of the force t o consider how forces such as electricity, magnetism, osmotic pressure, ordinary pressure, etc., become apparent only at a surface.


457

every other particle, but in the failure to see that this statement can only be true by the adjustment of a definite influence so as to include he universe within its scope. If the universe were a completely static system quite possibly the attractive influence proceeding from a particle would penetrate throughout the universe and this definite amount of attraction would be felt by (would be neutralized by) every other particle in the universe in proportion to its mass and inversely as the square of its distance. Newton’s law that the force between two particles

=

’?k

would be exactly true.

But no

less true would it be that if all of the attraction proceeding from the particles were sunimed up, it would be definite in amount and could be expressed by f

=

PW 1. S

completely static system both Newton’s law, f and the modification proposed, f

=

F”

Under this =

MM’

k s2 ’

7, are equally true,

one

having t o do with the totality of the force of the particle m, the other having to do with the distribution of this definite force. If now the million million particles immediately surrounding m be moved closer to m, the remaining universe staying as before, the modified law proposed as governing the total force of the particle m would remain unchanged. Newton’s law governing the distribution of the force could be applied as before after the system had become static. But it would have to be applied to a new system. The mass of all the particles in the universe with respect to m would have changed. It niight be possible to express this change merely as a change in “ k ” but of this I am very doubtful. The particles immediately surrounding m would now absorb more of its attraction than they did before. More remote particles would absorb less. Such at least is my conception of the relation between the usual law of gravitation and the law found to hold for molecu1a.r force.

458

J . E. Mills

21. Facts in accord with the suggested changes.-1. The connection between gravitation and mass or inertia is explained as being causal, or if one objects to the word “ causal,” they are merely different aspects of the same phenomenon. 2 . Since from the point of view outlined, mass or inertia is a necessary part of the gravitational attraction, the fact that the ether itself has no mass in the usual sense and is likewise devoid of attractive force is worthy of note. 3 . It has been long known that ether under certain conditions can react with matter, as evidenced by electrical, magnetic, gravitational, molecular, and light phenomena. That ether should offer no resistance to the motion of matter is an apparent fact that needs explanation none the less because scientists try to keep quiet about it. I have here suggested that the ether does offer resistance to the motion of matter, and that this resistance has to do with the field of force surrounding the body. I have shown that the usual definition and measure of mass is not independent of, but is dependent upon, the surrounding field of force. 4. Uniform motion in a circle has always proved a stumbling block.’ The usual explanation as to why the “falling body ” does not approach the center is perhaps satisfactory, but why the accelerated body does not increase in velocity under the action of the constant acceleration (in accordance with the law, velocity = acceleration X time) is far more difficult to understand. I think perhaps a more satisfactory explanation could be given by supposing that increased velocity of the body was prevented by the resistance that the ether offered to its motion. 5 . A basis is offered for explaining the fact that apparently gravitational force cannot be shielded, absorbed, or deflected, in any way. The idea is that the mass is a relative property and changes exactly in proportion to the change in the gravitational force. I took care to point out that in a vacuum a pound of lead, a gram of aluminum, and a feather all fell a t the same rate, and that if the mass of lead changed

“Science of Mechanism,” English translation, page 160.


459

to the mass of the feather during their fall no observation upon the motion of the bodies could detect the change. Apply this observation in toto t o a heavenly body. If by any means the mass of one heavenly body with reference to another was altered no observation upon the relative motion of the bodies could detect the change. 6. A basis is offered for explaining the fact that apparently gravitational force is propagated with infinite velocity, the explanation lying of course in the fact that the infinite velocity is only apparent. The alteration of mass and force takes place together and the finite velocity of propagation cannot be measured by the supposed method. 7. The gravitational force cannot be infinitely multiplied by the introduction of other particles into the field of force. The original field of force is simply readjusted, the total attractive force of each particle being perfectly definite in amount . 8. The law of gravitation comes into harmony with the law of the molecular attractive force. That the two forces are identically the same forces I have not yet proved. It may later be possible to show some relation between the constants of both forces. There are difficulties in the way of such identification. Perhaps the real solution of the identity lies yet deeper. The chemical force may be the ‘‘ left over” interatomic force ; the niolecular force the “ left over ” chemical force; the gravitational the “left over” molecular force. All may be one force governed by the same law-a readjustment of a definite force taking place with each combination. The fact that the intensity of the force seems to increase enormously from gravitational to molecular, from molecular to chemical, from chemical to interatomic (as judged by radium, etc.) lends some color to this supposition. Possibly electrical and magnetic forces are different manifestations of this same fundamental force-electricity being closely connected with the chemical force and magnetism with the molecular force. 9. It is impossible here to more than mention the similarity in the behavior of the electrical force and the

J . E. Mills

460

gravitational-molecular. as

charge

x

52

charge -

The electrical force is said to vary

, but in spite of this fact it is well recognized

that an electrical charge on a definite particle represents a definite amount of energy and that the above law-owing to the disturbance of the field of force-is not capable of indefinite extension. I think electrical and magnetic forces could be regarded as following a law similar to the one governing the molecular force. IO. The fact that a body attracts as though its mass were collected a t its center seems quite possible of explanation under the law of force given. I I . The fact that chemical changes, and ‘physical changes of temperature and energy content, have no effect upon weight is, from the point of view given, a matter for some surprise. One explanation of this fact has been suggested by Comstock. I 2 . The Cavendish experiment, and similar experiments, seem to indicate that consistent results under diverse conditions are obtained by writing the law of attraction, K

MM’

7-.

I am not satisfied as to the explanation of these experiments. I would only point out here: ( a ) That the experiments were nearly all performed with the idea of finding the gravitational constant, and the consequent density and weight of the earth, and usually without any intention of investigating the truth of the gravitational law. ( b ) The essence of each experiment consists in the determination of the earth’s attraction for two masses and a subsequent comparison of the attraction of the masses. The subsequent comparison of the attraction of the masses takes place in the earth’s field of force. (c) If the phenomena of electrical and magnetic attraction are considered as parallel phenomena it will be realized Jour. Am. Chem. SOC.,30, 683 (1908).

Molecular A ttraction

461

that the conclusion from these experiments, that substances attract always as the product of their masses, is yet open t o much doubt as regards its universal application. 13. Using the usual nomenclature the electrical force can be written ee ' charge X charge = Kff =K' S2

s2

*

The gravitational force can be written similarly, mm'

g =K-.

S2

Now if the forces are really identical we would havk, K'-

ee ' S2

=

mnz'

K-

sz

or

ee' --I

mm

=

constant,

a condition which is satisfied if elm = constant and e'/m'. = constant. From the point of view expressed in this paper the same result is reached yet more simply, the mass and the charge being measures of the same qQantity in different units. It would seem therefore that the important fact that the ratio of the charge of an electron to its mass is a constant can be cited as in agreement with the views expressed in this paper. In conclusion, I desire to say that in making the statements expressed in this paper I have not been actuated by any desire to startle or to change accepted usage. Starting originally with a research upon molecular attraction I have been led to the ideas expressed above as the best explanation of all the facts involved. Many things should be done that I have not yet been able to do. Particularly some quantitative method of testing the identity of gravitational and molecular forces should be devised. I am anxioas to have my views corrected where they are wrong and to have them developed where they prove to be right. Any criticism or help publicly or privately given will be greatly appreciated by the author. 22. Summary.-Attention is called to a law recently discovered by the author governing molecular attraction.

.,

462

J . E. Mills

The significance of this law is discussed and the law of the force deduced from it is compared with the law of the gravitational force. Careful examination of the facts would seem to indicate that perhaps the laws of gravitational and molecular force should be identical. It is shown that the gravitational law as proposed by Newton cannot apply to the molecular force and it is suggested that Newton’s statement of the law of gravitation should be modified so as to become f = s2

’

’ when the total force of mass

m is considered; that is,

gravitational attraction should be regarded as a definite property of matter, and not as a property indefinitely dependent upon the product of the masses. The evidence for the law of gravitation as stated by Newton is discussed and the difficulties involved in the usual view of gravitation are pointed out. Incidentally the other attractive forces, chemical, electrical, and magnetic, are discussed. The view is taken that possibly all of these forces are identical in origin and character. It is thought that the mass of a body is proportional t o the attraction exerted by it and that mass is a relative and not an absolute property of matter. The bearing of the ideas suggested upon a few points is briefly discussed. Camden, S. C., September 17, 1910

Molecular Attraction, IX. Molecular Attraction and the Law of Cravitation

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